SOLUTION: can you please explain this to me step by step so i can understand it. log(3-2x) - log (x+9)=0 i hope you can help me understand this thank you julie

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Question 119567: can you please explain this to me step by step so i can understand it.
log(3-2x) - log (x+9)=0
i hope you can help me understand this
thank you
julie
Found 2 solutions by jim_thompson5910, MaxLiebling:
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
log%2810%2C%283-2x%29%29-log%2810%2C%28x%2B9%29%29=0 Start with the given equation. Note: Since you did not specify a base, this means that we're going to use the default base 10.

log%2810%2C%28%283-2x%29%2F%28x%2B9%29%29%29=0 Combine the logs using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29




10%5E%280%29=%283-2x%29%2F%28x%2B9%29 Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> b%5Ey=x


1=%283-2x%29%2F%28x%2B9%29 Evaluate 10%5E%280%29 to get 1


x%2B9=3-2x Multiply both sides by x%2B9



x=3-2x-9Subtract 9 from both sides


x%2B2x=3-9 Add 2x to both sides


3x=3-9 Combine like terms on the left side


3x=-6 Combine like terms on the right side


x=%28-6%29%2F%283%29 Divide both sides by 3 to isolate x



x=-2 Divide

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Answer:
So our answer is x=-2

Answer by MaxLiebling(13) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given equation:
log%28%283-2x%29%29+-+log%28%28x%2B9%29%29+=+0
add log%28%28x%2B9%29%29 to both sides:
log%28%283-2x%29%29+=+log%28%28x%2B9%29%29
Note: logarithm is a strictly increasing function AND on both sides you have nothing but a Log(...) -> drop Log:
3-2x+=+x%2B9
add 2x-9 to both sides:
%283-2x%29+%2B+%282x-9%29+=+%28x%2B9%29+%2B+%282x-9%29
calculate left side:
%283-2x%29+%2B+%282x-9%29 = 3+%2B+%28-2x%2B2x%29-9%29 = 3+%2B+0+-9%29 = -6%29
calculate right side:
%28x%2B9%29+%2B+%282x-9%29 = %28x%2B2x%29+%2B+%289-9%29 = %28x%2B2x%29+%2B+0 = 3x%29
combine both sides:
-6%29 = 3x%29
that is:
3x+=+-6%29
divide both sides by 3:
x+=+-6%2F3%29
calculate -6%2F3%29 = -2%29
x+=+-2%29
proof left hand side:
log%28%283-2x%29%29 = log%28%283-2%2A%28-2%29%29%29 = log%28%283-%282%2A%28-2%29%29%29%29 = log%28%283-%28-4%29%29%29 = log%28%283%2B4%29%29 = log%28%287%29%29
proof right hand side:
log%28%28x%2B9%29%29 = log%28%28%28-2%29%2B9%29%29 = log%28%28-2%2B9%29%29 = log%28%287%29%29
both sides are equal: log%28%287%29%29